Remarks on universal nonsingular controls for discrete-time systems

Abstract

For analytic discrete-time systems, it is shown that uniform forward accessibility implies the generic existence of universal nonsingular control sequences. A particular application is given by considering forward accessible systems on compact manifolds. For general systems, it is proved that the complement of the set of universal sequences of infinite length is of the first category. For classes of systems satisfying a descending chain condition, and in particular, for systems defined by polynomial dynamics, forward accessibility implies uniform forward accessibility.